Newton's Law of Cooling

Wow, we can say that Newton is quite everywhere now. First we knew about him in Physics, now in Calculus. I wonder which other laws he made besides the laws of Gravity and of Cooling.

Anyways, here are my answers to some questions regarding this Law of Cooling, which we will use in the future for solving a murder case:

1. What is the Newton’s Law of Cooling?
"The rate of change in the temperature of an object is proportional to the difference between the object's temperature and the temperature of the surrounding environment". This is basically Newton's Law of Cooling. With this, Newton says that eventually, the temperature of an specific object and the temperature of the environment will eventually become equal.

2. What variables in your problem correspond with the variables in the Newton’s Law of Cooling?
Object variables:
t1: 9:10 PM(time of death of professor H)
t2: 9:16 PM (time when professor H's body temperature was at 95 degrees)
y1: 96 degrees (Professor H's body temperature)
y2: 95 degrees (Professor H's body temperature after 6 minutes)

Environment variables:
t1: 8:00 PM (time when the library was at 75 degrees)
t2: 9:00 PM (time when the library was at 70 degrees)
y1: 75 degrees (Library temperature at 9:00 PM)
y2: 70 degrees (Library temperature at 9:00 PM)

3. According to this Law, at what time approximately the death happened?
It occurred approximately between 8:50 PM and 8:55 PM. This is just an estimation, further investigation is required for determining the exact time of death

4. How does the room temperature affect the time of death?
Since the temperature of the object will become equal to the environment's temperature, we can deduce the the approximated time of dead depending on the next cases:
1. If the body temperature is considerably higher than the environment temperature, we can deduce that the time of death occurred during the last minutes
2. If the body temperature is close to the environment temperature, we can deduce that the time of death occurred time ago, ranging from hours to even days.

5. How does an illness (e.g. fever) affect the time of death?
Illness give the body abnormal temperature, generally higher temperatures. This affects the experts during the investigation of time of death because it will take more time for the body temperature to become equal to the environment temperature. For example, if the body is found with higher temperature than the environment's, then it wold appear that the body just died, but maybe the victim had fever and died hours ago, and it took more time to his body to balance with the environment temperature.

6. How exact is the approximation of the Newton’s Law of Cooling for predicting the time of death?
It's superbly exact. with Newton's Law of Cooling is possible to find almost the exact time of death of a person. If the calculation of the time of death is elaborated manually or with an standard calculator, the result may have maximum a 2% of error.